In many applications of intelligent computing, we need to choose an appropriate function – e.g., an appropriate re-scaling function, or an appropriate aggregation function. In applications of intelligent techniques, the problem of selecting an optimal function is usually too complex or too imprecise to be solved analytically, so the best functions are found empirically, by trying a large number of alternatives. In this paper, we show that in many such cases, the resulting empirical choice can be explained by natural invariance ideas. Example range from applications to building blocks of intelligent techniques – such as aggregation (including hierarchical aggregation) and averaging – to method-specific (polynomial fuzzy approach, pooling and averaging in deep learning) and domain-specific application, such as describing relative position of 2D and 3D objects, gauging segmentation quality, and perception of delay in public transportation.